Black line appears when rendering in cycles
Your hair mesh is going inside the face and due to that line is showing while render.

you may edit the hair mesh and pull outside few vertices to remove this line. 
So while you are in edit mode Edges should look like this:



Updated:
Problem area is seems to be here: 



These 2 vertices are going under the face mesh.

I cant reproduce the black line though, but here is how it might be issue and fix

Problem:



Grab these vertices :


Move vertices out of the face like this: